The energy of the universe is constant under the assumption that there are laws of physics that apply to the universe across all times (i.e. the motion of things in the universe can be explained without an explicit time dependence, like the gravitational constant shrinking with time without any underlying reason). Energy is the conserved quantity associated with time invariant laws of physics. So if you think energy is decreasing or increasing, you just have the wrong definition of energy (like when a ball rolling across the table slows down, it's lost energy, but really the energy has gone somewhere else).

It doesn't matter whether or not the system is relativistic - certainly energy is still conserved in special and general relativity. But I'd be curious if you could elaborate on what you were thinking there.

Another question: it is often said in, frankly mostly youtube videos, that in the very late universe "the expansion of the universe will rip apart atoms and eventually protons." So is this just completely wrong? I see the statement in your (2) reference saying that atoms do not, in fact have to "resist the temptation” to expand.

As a physicist who works nowhere near this field, this was a really enjoyable read. My first instinct was to ask about the cosmological redshift, which you addressed. But one thing I was concerned about that you didn't address was the accelerating expansion of spacetime.

Saul Perlmutter won the Nobel prize by using supernova standard candles to prove that the expansion of the universe was accelerating. Doesn't this indicate that the expansion of the universe is a real physical phenomenon - and that it certainly isn't just because of things moving generally apart from one another?

And what about all this discussion about the cosmological constant and vacuum energy (I think this is the same thing as my first question)? If the universe itself isn't expanding, why do we discuss a constant energy density throughout space that causes... an expansion.

CainIsmene gave a great answer. I'll just add one more general concept. Particles don't *just* annihlate on their respective antiparticle. First I have to define the conserved quantum numbers:

-charge

-baryon number (number of "matter" baryons - protons, neutrons, and other exotic ones minus number of antiprotons and antinuetrons)

-and lepton number (number of electrons+nuetrinos minus antielectrons and antineutrinos asterix we don't know if antineutrinos exist)

These three things, as far as we know, are perfectly conserved in nature. Now a useful definition of "annihilate": quickly turn into lower mass particles like electrons, muons, pions, or photons with a lot of kinetic energy. Annihilation occurs if you ever bring two particles into contact, and there exists any collection of lower mass particles with the same conserved quantum numbers. There is an important caveat, however, that in some cases two particles don't directly interact, which will stop them from annihilating (like a muon cant annihilate with an anti-electron until the muon decays into an electron, which takes about a microsecond, because there's no direct interaction between the two).
-So an antiproton and a neutron can annihilate because the baryon number of the system is zero and the charge of the system is -1. three pions, two negative charge and one positive charge have the same conserved quantum numbers. And there are plenty of particle interactions that allow that conversion. So they annihilate and make those pions.

One small caveat - neutrino/antineutrino "annihilations" have never been detected, and probably almost never happen in nature. There is a whole branch of experimental physics with 10s of large scale experiments looking for this process (neutrinoless double beta decay experiments). And there are scores of theoretical physicists developing theories in which neutrinos don't have antiparticles (Majorana neutrinos). People doubt neutrinos are majorana particles only because that would be odd - since all the other fermions are not majorana in the known universe.

I work on an experiment that traps antiprotons and we detect their presence by having them hit the wall of the trap (made of, obviously, normal matter) and we detect the charged pions. While these aren't antineutrons, it's the same exact concept. So yes this process is definitely observable.

Your answer seems to imply that if the system was spinning, you would call it higher temperature, because you can't "remove" the motion by going to the center of mass frame. I agree that it's useful to gasses to go to the center of mass frame to restore the distribution of velocities to a Maxwell-Boltzmann distribution so it looks more like a system with a well-defined temperature. However, I don't think there's anything in any reasonable definition of temperature that says "it's measured relative to the center of mass"

IDK what hospitals are doing, but I work in a physics lab, and nobody is ever letting their liquid helium just boil into the atmosphere unless something has gone catastrophically wrong. There's a whole infrastructure for recovering boiled off helium and sending it back to the liquefaction plant.

Forty__ gave a great answer. But just to add a more general conclusion. "Specific" usually means "per quantity of that thing." It doesn't necessarily need to be mass - although the two examples you gave are per mass. "Specific gravity" is a fancy word for density - or mass per volume.

And yeah its a horrible word. Doesn't make any sense with the normal English definition of specific. Old science terms are often bad science terms in modern English.